10. A natural number is greater than the
other by 5. The sum of their squares is 73. Find those numbers.
Sol. Let the second natural number be x.
∴ The first natural number is x + 5.
As per the given
condition,
x2 +
(x + 5)2 = 73
∴ x2 + x2 +
10x + 25 – 73 = 0
∴ 2x2 + 10x – 48 = 0
Dividing by 2, we
get
x2 +
5x – 24 = 0
∴ x2 – 3x + 8x – 24 = 0
∴ x (x – 3) + 8
(x – 3) = 0
∴ (x – 3) (x + 8)
= 0
∴ x – 3 = 0 or x
+ 8 = 0
∴x = 3 or x = - 8
∵ the natural
number cannot be negative
∴ x = 3
and x + 5 = 3 + 5
= 8
∴ the first
natural number is 8 and the second is 3.
